Arabi, C,

Bendahmane, A.

Conforti, M.

Kudlinski, A.

Mussot, A.

Vanvincq, O.

English

Archive Ouverte en Sciences de l'Information et de la Communication

   
Impact of higher-order dispersion on geometric parametric instability in 
GRIN multimode fibers 
 
A. Kudlinski1, A. Bendahmane1, O. Vanvincq1, C. Mas Arabi1, A. Mussot1 and M. Conforti1 
1.  University of Lille, CNRS, UMR 8523, PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France 
 
Light propagating in a graded-index (GRIN) multimode fiber experiences periodic self-imaging which can 
induce, at high intensity, a Kerr refractive index grating with a typical sub-millimeter period. This grating is at 
the origin of geometric parametric instability (GPI) [1], which has been observed only recently [2]. The 
frequency of the bands generated from this process are given by: 
𝛽𝛽𝑒𝑒(𝜔𝜔) + ?̅?𝛾𝑃𝑃 = 𝑘𝑘𝑘𝑘/𝑍𝑍, 
Where 𝛽𝛽𝑒𝑒(𝜔𝜔) =  ∑ 𝛽𝛽2𝑛𝑛(2𝑛𝑛)!𝑛𝑛≥1 (𝜔𝜔 − 𝜔𝜔0)𝑛𝑛 is the even part of dispersion relation, ?̅?𝛾 is the average nonlinear 
parameter (defined as in [3]), P is the pump power, Z is the period of self-imaging and 𝑘𝑘 ≥ 0 is an integer. GPI 
can therefore be seen as a quasi-phase matched four wave mixing (FWM) process. Many other FWM processes 
can coexist with GPI in a GRIN fiber, such as intermodal FWM [4], non-degenerate FWM between the pump 
and the first GPI band [5], or cascaded FWM of the first GPI band [6]. This makes experimental spectra very 
rich and complex, and it is often tricky to unambiguously identify the generated sidebands and their underlying 
generation mechanism. Usually, GPI sidebands are identified using relation (1) limited to second order 
dispersion (n = 1) [2]. A few studies considered higher-order dispersion (HOD)  [7], but its impact was not 
clearly illustrated. Here we show unambiguously that HOD plays a crucial role in the GPI process.  
To illustrate this, we plot in Fig. 1 (a) and (b) the roots of Eq. (1) for a when all even dispersion orders are 
taken into account in solid lines, and when only second order dispersion is considered in dotted lines. This is 
done for two different parabolic refractive index profiles with a maximum refractive index difference between 
the core and the cladding of ∆𝑛𝑛 = 20 × 10−3 (Fig. 1(c)) and ∆𝑛𝑛 = 33 × 10−3 (Fig. 1(d)). For both cases the 
pump wavelength is 1064 nm. 
Fig. 1 (a,b) Frequency detuning of the GPI sidebands vs. core diameter from Eq. (1). (c-d) Measured spectrum after 1 m 
propagation. See text for details.  
 
Two main conclusions can be drawn from these plots. First, for each value of k, two solutions appear for a given 
core radius when HOD is taken into account, while there is only one with second order dispersion. Second, there 
is a core radius value (around 25 µm in both cases) under which no GPI can be observed when HOD is taken 
into account. This threshold cannot be seen when only second order dispersion is considered. Experiments 
(depicted by markers in Figs 1(a) and (b)) were performed to confirm this. Typical experimental spectra are 
displayed in Figs. 1 (c) and (d), at low power (10 kW) in blue and high power (40 kW) in red. At low power, 
well isolated GPI sidebands can be easily identified and match the theoretical curves pretty well. At high power, 
we checked that additional sideband appearing do not originate from GPI, but rather from the other mechanisms 
listed above. An unambiguous identification of all spectral peaks observed in the experiment will be detailed 
during the conference.  
References 
[1] S. Longhi, "Modulational instability and space time dynamics in nonlinear parabolic-index optical fibers," Opt. Lett. 28, 2363 (2003). 
[2] K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, "Observation of 
Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves," Phys. Rev. Lett. 116, 183901 (2016). 
[3] M. Conforti, C. Mas Arabi, A. Mussot, and A. Kudlinski, "Fast and accurate modeling of nonlinear pulse propagation in graded-index 
multimode fibers," Opt. Lett. 42, 4004 (2017). 
[4] E. Nazemosadat, H. Pourbeyram, and A. Mafi, "Phase matching for spontaneous frequency conversion via four-wave mixing in graded-
index multimode optical fibers," J. Opt. Soc. Am. B 33, 144 (2016). 
[5] R. Dupiol, A. Bendahmane, K. Krupa, J. Fatome, A. Tonello, M. Fabert, V. Couderc, S. Wabnitz, and G. Millot, "Intermodal 
modulational instability in graded-index multimode optical fibers," Opt. Lett. 42, 3419 (2017). 
[6] R. Dupiol, A. Bendahmane, K. Krupa, A. Tonello, M. Fabert, B. Kibler, T. Sylvestre, A. Barthelemy, V. Couderc, S. Wabnitz, and G. 
Millot, "Far-detuned cascaded intermodal four-wave mixing in a multimode fiber," Opt. Lett. 42, 1293 (2017). 
[7] H. E. Lopez-Aviles, F. O. Wu, Z. Sanjabi Eznaveh, M. A. Eftekhar, F. Wise, R. Amezcua Correa, and D. N. Christodoulides, "A 
systematic analysis of parametric instabilities in nonlinear parabolic multimode fibers," APL Photonics 4, 022803 (2019). 
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Impact of higher-order dispersion on geometric parametric instability in GRIN multimode fibers

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Impact of higher-order dispersion on geometric parametric instability in GRIN multimode fibers

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